The parametric equations $x=2a\cot(\theta),\;\;y=2a\sin^2(\theta)$ describe the curve known as the witch of Maria Agnesi. With $a = 3$, use Simpson's rule with $n = 4$ to estimate the length of the arc of this curve given by $\pi/4 \le \theta \le \pi/2.$ Make sure your answer is correct to three decimal places.

Length of arc $\approx$